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Volumn 30, Issue 1-2, 1998, Pages 5-25

An invariance principle for semimartingale reflecting Brownian motions in an orthant

Author keywords

Diffusions; Invariance principle; Open multiclass queueing networks; Oscillation inequality; Semimartingale reflecting Brownian motion; Skorokhod problem

Indexed keywords

BROWNIAN MOVEMENT; DIFFUSION; QUEUEING THEORY;

EID: 0032260551     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/a:1019156702875     Document Type: Article
Times cited : (75)

References (27)
  • 2
    • 0032262849 scopus 로고    scopus 로고
    • State space collapse with application to heavy traffic limits for multiclass queueing networks
    • M. Bramson, State space collapse with application to heavy traffic limits for multiclass queueing networks, Queueing Systems 30 (1998) 89-148.
    • (1998) Queueing Systems , vol.30 , pp. 89-148
    • Bramson, M.1
  • 3
    • 0040750211 scopus 로고    scopus 로고
    • Diffusion approximations for re-entrant lines with a first-buffer-first-served priority discipline
    • H. Chen and H. Zhang, Diffusion approximations for re-entrant lines with a first-buffer-first-served priority discipline, Queueing Systems 23 (1996) 177-195.
    • (1996) Queueing Systems , vol.23 , pp. 177-195
    • Chen, H.1    Zhang, H.2
  • 4
    • 84872999204 scopus 로고    scopus 로고
    • A heavy traffic limit theorem for a class of open queueing networks with finite buffers
    • submitted
    • J.G. Dai and W. Dai, A heavy traffic limit theorem for a class of open queueing networks with finite buffers, submitted to Queueing Systems (1997).
    • (1997) Queueing Systems
    • Dai, J.G.1    Dai, W.2
  • 5
    • 0002973242 scopus 로고
    • On the convergence of multiclass queueing networks in heavy traffic
    • J.G. Dai and V. Nguyen, On the convergence of multiclass queueing networks in heavy traffic, Ann. Appl. Probab. 4 (1994) 26-42.
    • (1994) Ann. Appl. Probab. , vol.4 , pp. 26-42
    • Dai, J.G.1    Nguyen, V.2
  • 6
    • 0003124563 scopus 로고
    • Nonexistence of Brownian models of certain multiclass queueing networks
    • J.G. Dai and Y. Wang, Nonexistence of Brownian models of certain multiclass queueing networks, Queueing Systems 13 (1993) 41-46.
    • (1993) Queueing Systems , vol.13 , pp. 41-46
    • Dai, J.G.1    Wang, Y.2
  • 7
    • 0002611604 scopus 로고
    • Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons
    • J.G. Dai and R.J. Williams, Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons, Theory Probab. Appl. 40 (1995) 1-40.
    • (1995) Theory Probab. Appl. , vol.40 , pp. 1-40
    • Dai, J.G.1    Williams, R.J.2
  • 9
    • 0001985427 scopus 로고
    • On the Lipschitz continuity of the solution mapping to the Skorokhod problem
    • P. Dupuis and H. Ishii, On the Lipschitz continuity of the solution mapping to the Skorokhod problem, Stochastics and Stochastics Rep. 35 (1991) 31-62.
    • (1991) Stochastics and Stochastics Rep. , vol.35 , pp. 31-62
    • Dupuis, P.1    Ishii, H.2
  • 11
    • 0000625769 scopus 로고    scopus 로고
    • The BIGSTEP approach to flow management in stochastic processing networks
    • eds. F.P. Kelly, S. Zachary and I. Ziedins Oxford Univ. Press, Oxford
    • J.M. Harrison, The BIGSTEP approach to flow management in stochastic processing networks, in: Stochastic Networks: Theory and Applications, eds. F.P. Kelly, S. Zachary and I. Ziedins (Oxford Univ. Press, Oxford, 1996) pp. 57-90.
    • (1996) Stochastic Networks: Theory and Applications , pp. 57-90
    • Harrison, J.M.1
  • 12
    • 0000585232 scopus 로고
    • Reflected Brownian motion on an orthant
    • J.M. Harrison and M.I. Reiman, Reflected Brownian motion on an orthant, Ann. Probab. 9 (1981) 302-308.
    • (1981) Ann. Probab. , vol.9 , pp. 302-308
    • Harrison, J.M.1    Reiman, M.I.2
  • 13
    • 0001109907 scopus 로고
    • Scheduling networks of queues: Heavy traffic analysis of a simple open network
    • J.M. Harrison and L.M. Wein, Scheduling networks of queues: Heavy traffic analysis of a simple open network, Queueing Systems 5 (1989) 265-280.
    • (1989) Queueing Systems , vol.5 , pp. 265-280
    • Harrison, J.M.1    Wein, L.M.2
  • 14
    • 0002415784 scopus 로고
    • Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling
    • F.P. Kelly and C.N. Laws, Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling, Queueing Systems 13 (1993) 47-86.
    • (1993) Queueing Systems , vol.13 , pp. 47-86
    • Kelly, F.P.1    Laws, C.N.2
  • 17
    • 0002816593 scopus 로고
    • Diffusion approximations for networks of queues with multiple customer types
    • W.P. Peterson, Diffusion approximations for networks of queues with multiple customer types, Math. Oper. Res. 9 (1991) 90-118.
    • (1991) Math. Oper. Res. , vol.9 , pp. 90-118
    • Peterson, W.P.1
  • 18
    • 0021481522 scopus 로고
    • Open queueing networks in heavy traffic
    • M.I. Reiman, Open queueing networks in heavy traffic, Math. Oper. Res. 9 (1984) 441-458.
    • (1984) Math. Oper. Res. , vol.9 , pp. 441-458
    • Reiman, M.I.1
  • 19
    • 0002800360 scopus 로고
    • A boundary property of semimartingale reflecting Brownian motions
    • M.I. Reiman and R.J. Williams, A boundary property of semimartingale reflecting Brownian motions, Probab. Theory Related Fields 77 (1988) 87-97, and 80 (1989) 633.
    • (1988) Probab. Theory Related Fields , vol.77 , pp. 87-97
    • Reiman, M.I.1    Williams, R.J.2
  • 20
    • 0002800360 scopus 로고
    • M.I. Reiman and R.J. Williams, A boundary property of semimartingale reflecting Brownian motions, Probab. Theory Related Fields 77 (1988) 87-97, and 80 (1989) 633.
    • (1989) Probab. Theory Related Fields , vol.80 , pp. 633
  • 21
    • 0001380311 scopus 로고
    • Limit theorems for stochastic processes
    • A.V. Skorokhod, Limit theorems for stochastic processes, Theory Probab. Appl. 1 (1956) 261-290.
    • (1956) Theory Probab. Appl. , vol.1 , pp. 261-290
    • Skorokhod, A.V.1
  • 23
    • 84980153169 scopus 로고
    • Diffusion processes with boundary conditions
    • D.W. Stroock and S.R.S. Varadhan, Diffusion processes with boundary conditions, Comm. Pure Appl. Math. 24 (1971) 147-225.
    • (1971) Comm. Pure Appl. Math. , vol.24 , pp. 147-225
    • Stroock, D.W.1    Varadhan, S.R.S.2
  • 24
    • 21144473462 scopus 로고
    • Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant
    • L.M. Taylor and R.J. Williams, Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant, Probab. Theory Related Fields 96 (1993) 283-317.
    • (1993) Probab. Theory Related Fields , vol.96 , pp. 283-317
    • Taylor, L.M.1    Williams, R.J.2
  • 25
    • 0027644551 scopus 로고
    • Large fluctuations in a deterministic multiclass network of queues
    • W. Whitt, Large fluctuations in a deterministic multiclass network of queues, Managm. Sci. 39 (1993) 1020-1028.
    • (1993) Managm. Sci. , vol.39 , pp. 1020-1028
    • Whitt, W.1
  • 26
    • 0002248871 scopus 로고    scopus 로고
    • On the approximation of queueing networks in heavy traffic
    • eds. F.P. Kelly, S. Zachary and I. Ziedins Oxford Univ. Press, Oxford
    • R.J. Williams, On the approximation of queueing networks in heavy traffic, in: Stochastic Networks: Theory and Applications, eds. F.P. Kelly, S. Zachary and I. Ziedins (Oxford Univ. Press, Oxford, 1996) pp. 35-56.
    • (1996) Stochastic Networks: Theory and Applications , pp. 35-56
    • Williams, R.J.1
  • 27
    • 0032262848 scopus 로고    scopus 로고
    • Diffusion approximations for open multiclass queueing networks: Sufficient conditions involving state space collapse
    • R.J. Williams, Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse, Queueing Systems 30 (1998) 27-88.
    • (1998) Queueing Systems , vol.30 , pp. 27-88
    • Williams, R.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.